where \(q_\phi (\mathbf {z}\vert \mathbf {x})\)  is the encoder that maps a sample \(\mathbf {x}\)  to a latent code \(\mathbf {z}\)  and \(p_\theta (\mathbf {x}\vert \mathbf {z})\)  is the probabilistic decoder that can generate observations from seen/unseen latent codes, which are both parameterized by neural networks with learnable parameters \(\phi \)  and \(\theta \) , respectively.
Such modification of the VAE objective (ELBO) is shown effective for learning disentangled representations [1]} as the \(\beta \)  value helps to achieve less correlation between the latent dimensions, resulting semantically more meaningful latent codes [2]}, [3]}, [4]}.

